Vol. 302, No. 2, 2019

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$\tau$-tilting finite gentle algebras are representation-finite

Pierre-Guy Plamondon

Vol. 302 (2019), No. 2, 709–716
Abstract

We show that a gentle algebra over a field is $\tau$-tilting finite if and only if it is representation-finite. The proof relies on the “brick-$\tau$-tilting correspondence” of Demonet, Iyama, and Jasso and on a combinatorial analysis.

Keywords
representation theory, $\tau$-tilting theory, finite representation type, gentle algebras
Primary: 16G20
Secondary: 16G60
Milestones
Revised: 23 March 2019
Accepted: 23 March 2019
Published: 27 November 2019
Authors
 Pierre-Guy Plamondon Laboratoire de Mathématique d’Orsay Université Paris-Sud Centre National de la Recherche Scientifique Université Paris-Saclay Orsay France